Contract Source Code:
// SPDX-License-Identifier: MIT
pragma solidity >=0.6.0 <0.8.0;
/**
* @dev Interface of the ERC20 standard as defined in the EIP.
*/
interface IERC20 {
/**
* @dev Returns the amount of tokens in existence.
*/
function totalSupply() external view returns (uint256);
/**
* @dev Returns the amount of tokens owned by `account`.
*/
function balanceOf(address account) external view returns (uint256);
/**
* @dev Moves `amount` tokens from the caller's account to `recipient`.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transfer(address recipient, uint256 amount) external returns (bool);
/**
* @dev Returns the remaining number of tokens that `spender` will be
* allowed to spend on behalf of `owner` through {transferFrom}. This is
* zero by default.
*
* This value changes when {approve} or {transferFrom} are called.
*/
function allowance(address owner, address spender) external view returns (uint256);
/**
* @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* IMPORTANT: Beware that changing an allowance with this method brings the risk
* that someone may use both the old and the new allowance by unfortunate
* transaction ordering. One possible solution to mitigate this race
* condition is to first reduce the spender's allowance to 0 and set the
* desired value afterwards:
* https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
*
* Emits an {Approval} event.
*/
function approve(address spender, uint256 amount) external returns (bool);
/**
* @dev Moves `amount` tokens from `sender` to `recipient` using the
* allowance mechanism. `amount` is then deducted from the caller's
* allowance.
*
* Returns a boolean value indicating whether the operation succeeded.
*
* Emits a {Transfer} event.
*/
function transferFrom(address sender, address recipient, uint256 amount) external returns (bool);
/**
* @dev Emitted when `value` tokens are moved from one account (`from`) to
* another (`to`).
*
* Note that `value` may be zero.
*/
event Transfer(address indexed from, address indexed to, uint256 value);
/**
* @dev Emitted when the allowance of a `spender` for an `owner` is set by
* a call to {approve}. `value` is the new allowance.
*/
event Approval(address indexed owner, address indexed spender, uint256 value);
}
// SPDX-License-Identifier: Unlicense
pragma solidity =0.6.8;
import "../interfaces/IEmpireERC20.sol";
import "../libraries/common/EmpireMath.sol";
contract EmpireERC20 is IEmpireERC20 {
using EmpireMath for uint256;
string public constant override name = "Empire LP";
string public constant override symbol = "EMP-LP";
uint8 public constant override decimals = 18;
uint256 public override totalSupply;
mapping(address => uint256) public override balanceOf;
mapping(address => mapping(address => uint256)) public override allowance;
uint256 private immutable CACHED_CHAIN_ID;
bytes32 private immutable CACHED_DOMAIN_SEPARATOR;
bytes32 private constant EIP712_DOMAIN =
keccak256(
"EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"
);
bytes32 private constant PERMIT_TYPEHASH =
keccak256(
"Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)"
);
mapping(address => uint256) public override nonces;
event Approval(
address indexed owner,
address indexed spender,
uint256 value
);
event Transfer(address indexed from, address indexed to, uint256 value);
constructor() public {
uint256 chainId;
assembly {
chainId := chainid()
}
CACHED_CHAIN_ID = chainId;
CACHED_DOMAIN_SEPARATOR = _computeSeparator(chainId);
}
function _mint(address to, uint256 value) internal {
totalSupply = totalSupply.add(value);
balanceOf[to] = balanceOf[to].add(value);
emit Transfer(address(0), to, value);
}
function _burn(address from, uint256 value) internal {
balanceOf[from] = balanceOf[from].sub(value);
totalSupply = totalSupply.sub(value);
emit Transfer(from, address(0), value);
}
function _approve(
address owner,
address spender,
uint256 value
) private {
allowance[owner][spender] = value;
emit Approval(owner, spender, value);
}
function _transfer(
address from,
address to,
uint256 value
) private {
balanceOf[from] = balanceOf[from].sub(value);
balanceOf[to] = balanceOf[to].add(value);
emit Transfer(from, to, value);
}
function approve(address spender, uint256 value)
external
override
returns (bool)
{
_approve(msg.sender, spender, value);
return true;
}
function transfer(address to, uint256 value)
external
override
returns (bool)
{
_transfer(msg.sender, to, value);
return true;
}
function transferFrom(
address from,
address to,
uint256 value
) external override returns (bool) {
if (allowance[from][msg.sender] != uint256(-1)) {
allowance[from][msg.sender] = allowance[from][msg.sender].sub(
value
);
}
_transfer(from, to, value);
return true;
}
function _computeSeparator(uint256 chainId)
internal
view
returns (bytes32)
{
return
keccak256(
abi.encode(
EIP712_DOMAIN,
keccak256(bytes(name)),
keccak256(bytes("1")),
chainId,
address(this)
)
);
}
function _getDigest(bytes32 payload) internal view returns (bytes32) {
uint256 chainId;
assembly {
chainId := chainid()
}
bytes32 domainSeparator =
chainId != CACHED_CHAIN_ID
? _computeSeparator(chainId)
: CACHED_DOMAIN_SEPARATOR;
return
keccak256(abi.encodePacked("\x19\x01", domainSeparator, payload));
}
function permit(
address owner,
address spender,
uint256 value,
uint256 deadline,
uint8 v,
bytes32 r,
bytes32 s
) external override {
require(deadline >= block.timestamp, "Empire: EXPIRED");
bytes32 digest =
_getDigest(
keccak256(
abi.encode(
PERMIT_TYPEHASH,
owner,
spender,
value,
nonces[owner]++,
deadline
)
)
);
address recoveredAddress = ecrecover(digest, v, r, s);
require(
recoveredAddress != address(0) && recoveredAddress == owner,
"Empire: INVALID_SIGNATURE"
);
_approve(owner, spender, value);
}
}
// SPDX-License-Identifier: Unlicense
pragma solidity =0.6.8;
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "../interfaces/IEmpirePair.sol";
import "../interfaces/IEmpireFactory.sol";
import "../interfaces/IEmpireCallee.sol";
import "../libraries/dex/UQ112x112.sol";
import "./EmpireERC20.sol";
contract EmpirePair is IEmpirePair, EmpireERC20 {
using UQ112x112 for uint224;
uint256 private constant MINIMUM_LIQUIDITY = 10**3;
bytes4 private constant TRANSFER_SELECTOR =
bytes4(keccak256(bytes("transfer(address,uint256)")));
bytes4 private constant TRANSFER_FROM_SELECTOR =
bytes4(keccak256(bytes("transferFrom(address,address,uint256)")));
address public immutable override factory;
address public override token0;
address public override token1;
uint112 private override reserve0; // uses single storage slot, accessible via getReserves
uint112 private override reserve1; // uses single storage slot, accessible via getReserves
uint32 private override blockTimestampLast; // uses single storage slot, accessible via getReserves
uint256 public override price0CumulativeLast;
uint256 public override price1CumulativeLast;
uint256 public override kLast; // reserve0 * reserve1, as of immediately after the most recent liquidity event
uint256 public override liquidityLocked; // By default, liquidity is not locked (timestamp is 0)
address public override sweepableToken; // By default, no token is sweepable
uint256 public override sweptAmount; // Tracks how many tokens were swept based on the floor price
PairType public empirePairType; // Tracks pair type
uint256 public empireLockTime; // Tracks lock time
uint256 private unlocked = 1;
modifier lock() {
require(unlocked == 1, "Empire: LOCKED");
unlocked = 2;
_;
unlocked = 1;
}
function getReserves()
public
view
override
returns (
uint112 _reserve0,
uint112 _reserve1,
uint32 _blockTimestampLast
)
{
_reserve0 = reserve0;
_reserve1 = reserve1;
_blockTimestampLast = blockTimestampLast;
}
function _safeTransfer(
address token,
address to,
uint256 value
) private {
_safeCall(token, abi.encodeWithSelector(TRANSFER_SELECTOR, to, value));
}
function _safeTransferFrom(
address token,
address from,
address to,
uint256 value
) private {
_safeCall(
token,
abi.encodeWithSelector(TRANSFER_FROM_SELECTOR, from, to, value)
);
}
function _safeCall(address token, bytes memory payload) private {
(bool success, bytes memory data) = token.call(payload);
require(
success && (data.length == 0 || abi.decode(data, (bool))),
"Empire: TRANSFER_FAILED"
);
}
event Mint(address indexed sender, uint256 amount0, uint256 amount1);
event Burn(
address indexed sender,
uint256 amount0,
uint256 amount1,
address indexed to
);
event Swap(
address indexed sender,
uint256 amount0In,
uint256 amount1In,
uint256 amount0Out,
uint256 amount1Out,
address indexed to
);
event Sync(uint112 reserve0, uint112 reserve1);
event Swept(uint256 amount);
event Unswept(uint256 amount);
constructor() public {
factory = msg.sender;
}
// called once by the factory at time of deployment
function initialize(
address _token0,
address _token1,
PairType pairType,
uint256 unlockTime
) external override {
require(msg.sender == factory, "Empire: FORBIDDEN"); // sufficient check
token0 = _token0;
token1 = _token1;
if (pairType != PairType.Common) {
liquidityLocked = unlockTime;
empirePairType = pairType;
if (pairType == PairType.SweepableToken0) {
sweepableToken = _token0;
} else if (pairType == PairType.SweepableToken1) {
sweepableToken = _token1;
}
}
empireLockTime = unlockTime;
}
// update reserves and, on the first call per block, price accumulators
function _update(
uint256 balance0,
uint256 balance1,
uint112 _reserve0,
uint112 _reserve1
) private {
require(
balance0 <= uint112(-1) && balance1 <= uint112(-1),
"Empire: OVERFLOW"
);
uint32 blockTimestamp = uint32(block.timestamp % 2**32);
uint32 timeElapsed = blockTimestamp - blockTimestampLast; // overflow is desired
if (timeElapsed > 0 && _reserve0 != 0 && _reserve1 != 0) {
// * never overflows, and + overflow is desired
price0CumulativeLast +=
uint256(UQ112x112.encode(_reserve1).uqdiv(_reserve0)) *
timeElapsed;
price1CumulativeLast +=
uint256(UQ112x112.encode(_reserve0).uqdiv(_reserve1)) *
timeElapsed;
}
reserve0 = uint112(balance0);
reserve1 = uint112(balance1);
blockTimestampLast = blockTimestamp;
emit Sync(reserve0, reserve1);
}
// if fee is on, mint liquidity equivalent to 1/6th of the growth in sqrt(k)
function _mintFee(uint112 _reserve0, uint112 _reserve1)
private
returns (bool feeOn)
{
address feeTo = IEmpireFactory(factory).feeTo();
feeOn = feeTo != address(0);
uint256 _kLast = kLast; // gas savings
if (feeOn) {
if (_kLast != 0) {
uint256 rootK = uint256(_reserve0).mul(_reserve1).sqrt();
uint256 rootKLast = _kLast.sqrt();
if (rootK > rootKLast) {
uint256 numerator = totalSupply.mul(rootK.sub(rootKLast));
uint256 denominator = rootK.mul(5).add(rootKLast);
uint256 liquidity = numerator / denominator;
if (liquidity > 0) _mint(feeTo, liquidity);
}
}
} else if (_kLast != 0) {
kLast = 0;
}
}
// this low-level function should be called from a contract which performs important safety checks
function mint(address to)
external
override
lock
returns (uint256 liquidity)
{
(uint112 _reserve0, uint112 _reserve1, ) = getReserves(); // gas savings
uint256 balance0 = _balanceOfSelf(token0);
uint256 balance1 = _balanceOfSelf(token1);
uint256 amount0 = balance0.sub(_reserve0);
uint256 amount1 = balance1.sub(_reserve1);
bool feeOn = _mintFee(_reserve0, _reserve1);
uint256 _totalSupply = totalSupply; // gas savings, must be defined here since totalSupply can update in _mintFee
if (_totalSupply == 0) {
liquidity = amount0.mul(amount1).sqrt().sub(MINIMUM_LIQUIDITY);
_mint(address(0), MINIMUM_LIQUIDITY); // permanently lock the first MINIMUM_LIQUIDITY tokens
} else {
liquidity = (amount0.mul(_totalSupply) / _reserve0).min(
amount1.mul(_totalSupply) / _reserve1
);
}
require(liquidity > 0, "Empire: INSUFFICIENT_LIQUIDITY_MINTED");
_mint(to, liquidity);
_update(balance0, balance1, _reserve0, _reserve1);
if (feeOn) kLast = uint256(reserve0).mul(reserve1); // reserve0 and reserve1 are up-to-date
emit Mint(msg.sender, amount0, amount1);
}
// this low-level function should be called from a contract which performs important safety checks
function burn(address to)
external
override
lock
returns (uint256 amount0, uint256 amount1)
{
require(block.timestamp >= liquidityLocked, "Empire: LIQUIDITY_LOCKED");
(uint112 _reserve0, uint112 _reserve1, ) = getReserves(); // gas savings
address _token0 = token0; // gas savings
address _token1 = token1; // gas savings
uint256 balance0 = _balanceOfSelf(_token0);
uint256 balance1 = _balanceOfSelf(_token1);
uint256 liquidity = balanceOf[address(this)];
bool feeOn = _mintFee(_reserve0, _reserve1);
uint256 _totalSupply = totalSupply; // gas savings, must be defined here since totalSupply can update in _mintFee
amount0 = liquidity.mul(balance0) / _totalSupply; // using balances ensures pro-rata distribution
amount1 = liquidity.mul(balance1) / _totalSupply; // using balances ensures pro-rata distribution
require(
amount0 > 0 && amount1 > 0,
"Empire: INSUFFICIENT_LIQUIDITY_BURNED"
);
_burn(address(this), liquidity);
_safeTransfer(_token0, to, amount0);
_safeTransfer(_token1, to, amount1);
balance0 = _balanceOfSelf(_token0);
balance1 = _balanceOfSelf(_token1);
_update(balance0, balance1, _reserve0, _reserve1);
if (feeOn) kLast = uint256(reserve0).mul(reserve1); // reserve0 and reserve1 are up-to-date
emit Burn(msg.sender, amount0, amount1, to);
}
// this low-level function should be called from a contract which performs important safety checks
function swap(
uint256 amount0Out,
uint256 amount1Out,
address to,
bytes calldata data
) external override lock {
require(
amount0Out > 0 || amount1Out > 0,
"Empire: INSUFFICIENT_OUTPUT_AMOUNT"
);
(uint112 _reserve0, uint112 _reserve1, ) = getReserves(); // gas savings
require(
amount0Out < _reserve0 && amount1Out < _reserve1,
"Empire: INSUFFICIENT_LIQUIDITY"
);
uint256 balance0;
uint256 balance1;
{
// scope for _token{0,1}, avoids stack too deep errors
address _token0 = token0;
address _token1 = token1;
require(to != _token0 && to != _token1, "Empire: INVALID_TO");
if (amount0Out > 0) _safeTransfer(_token0, to, amount0Out); // optimistically transfer tokens
if (amount1Out > 0) _safeTransfer(_token1, to, amount1Out); // optimistically transfer tokens
if (data.length > 0)
IEmpireCallee(to).empireCall(
msg.sender,
amount0Out,
amount1Out,
data
);
balance0 = _balanceOfSelf(_token0);
balance1 = _balanceOfSelf(_token1);
}
uint256 amount0In =
balance0 > _reserve0 - amount0Out
? balance0 - (_reserve0 - amount0Out)
: 0;
uint256 amount1In =
balance1 > _reserve1 - amount1Out
? balance1 - (_reserve1 - amount1Out)
: 0;
require(
amount0In > 0 || amount1In > 0,
"Empire: INSUFFICIENT_INPUT_AMOUNT"
);
{
// scope for reserve{0,1}Adjusted, avoids stack too deep errors
uint256 balance0Adjusted = balance0.mul(1000).sub(amount0In.mul(3));
uint256 balance1Adjusted = balance1.mul(1000).sub(amount1In.mul(3));
require(
balance0Adjusted.mul(balance1Adjusted) >=
uint256(_reserve0).mul(_reserve1).mul(1000**2),
"Empire: K"
);
}
_update(balance0, balance1, _reserve0, _reserve1);
emit Swap(msg.sender, amount0In, amount1In, amount0Out, amount1Out, to);
}
// force balances to match reserves
function skim(address to) external override lock {
address _token0 = token0; // gas savings
address _token1 = token1; // gas savings
_safeTransfer(_token0, to, _balanceOfSelf(_token0).sub(reserve0));
_safeTransfer(_token1, to, _balanceOfSelf(_token1).sub(reserve1));
}
// force reserves to match balances
function sync() external override lock {
_update(
_balanceOfSelf(token0),
_balanceOfSelf(token1),
reserve0,
reserve1
);
}
// wrapper ensuring sweeps are accounted for
function _balanceOfSelf(address token)
internal
view
returns (uint256 balance)
{
if (token == sweepableToken) {
balance = sweptAmount;
}
return balance.add(IERC20(token).balanceOf(address(this)));
}
// allow sweeping if enabled
function sweep(uint256 amount, bytes calldata data) external override lock {
address _token0 = token0;
address _token1 = token1;
uint256 _reserveSwept;
uint256 _reserveSweeper;
if (msg.sender == _token0) {
require(sweepableToken == _token1, "Empire: INCORRECT_CALLER");
_reserveSwept = reserve1;
_reserveSweeper = reserve0;
} else {
require(
msg.sender == _token1 && sweepableToken == _token0,
"Empire: INCORRECT_CALLER"
);
_reserveSwept = reserve0;
_reserveSweeper = reserve1;
}
// Calculate necessary sweepable token amount for pool to contain full token supply
uint256 amountIn = IERC20(msg.sender).totalSupply() - _reserveSweeper;
uint256 numerator = amountIn.mul(_reserveSwept);
uint256 denominator = _reserveSweeper.mul(1000).add(amountIn);
uint256 amountOut = numerator / denominator;
uint256 maxSweepable = _reserveSwept - amountOut;
uint256 _sweptAmount = sweptAmount.add(amount);
require(_sweptAmount <= maxSweepable, "Empire: INCORRECT_SWEEP_AMOUNT");
sweptAmount = _sweptAmount;
_safeTransfer(sweepableToken, msg.sender, amount);
IEmpireCallee(msg.sender).empireSweepCall(amount, data);
emit Swept(amount);
}
function unsweep(uint256 amount) external override lock {
address _token0 = token0;
address _token1 = token1;
if (msg.sender == _token0) {
require(sweepableToken == _token1, "Empire: INCORRECT_CALLER");
} else {
require(
msg.sender == _token1 && sweepableToken == _token0,
"Empire: INCORRECT_CALLER"
);
}
_safeTransferFrom(sweepableToken, msg.sender, address(this), amount);
sweptAmount = sweptAmount.sub(amount);
emit Unswept(amount);
}
function getMaxSweepable() external view override returns (uint256) {
address _token0 = token0;
address _token1 = token1;
address _sweeper;
uint256 _reserveIn;
uint256 _reserveOut;
if (sweepableToken == _token0) {
_sweeper = _token1;
_reserveIn = reserve1;
_reserveOut = reserve0;
} else {
require(sweepableToken == token1, "Empire: NON_SWEEPABLE_POOL");
_sweeper = _token0;
_reserveIn = reserve0;
_reserveOut = reserve1;
}
uint256 amountIn = IERC20(_sweeper).totalSupply() - _reserveIn;
uint256 amountOut = getAmountOut(amountIn, _reserveIn, _reserveOut);
return _reserveOut - amountOut;
}
function getAmountOut(
uint256 amountIn,
uint256 reserveIn,
uint256 reserveOut
) internal pure returns (uint256 amountOut) {
if (amountIn == 0) return 0;
uint256 amountInWithFee = amountIn.mul(997);
uint256 numerator = amountInWithFee.mul(reserveOut);
uint256 denominator = reserveIn.mul(1000).add(amountInWithFee);
amountOut = numerator / denominator;
}
}
// SPDX-License-Identifier: Unlicense
pragma solidity =0.6.8;
interface IEmpireCallee {
function empireCall(
address sender,
uint256 amount0,
uint256 amount1,
bytes calldata data
) external;
function empireSweepCall(uint256 amountSwept, bytes calldata data) external;
}
// SPDX-License-Identifier: Unlicense
pragma solidity =0.6.8;
interface IEmpireERC20 {
event Approval(
address indexed owner,
address indexed spender,
uint256 value
);
event Transfer(address indexed from, address indexed to, uint256 value);
function name() external pure returns (string memory);
function symbol() external pure returns (string memory);
function decimals() external pure returns (uint8);
function totalSupply() external view returns (uint256);
function balanceOf(address owner) external view returns (uint256);
function allowance(address owner, address spender)
external
view
returns (uint256);
function approve(address spender, uint256 value) external returns (bool);
function transfer(address to, uint256 value) external returns (bool);
function transferFrom(
address from,
address to,
uint256 value
) external returns (bool);
function nonces(address owner) external view returns (uint256);
function permit(
address owner,
address spender,
uint256 value,
uint256 deadline,
uint8 v,
bytes32 r,
bytes32 s
) external;
}
// SPDX-License-Identifier: Unlicense
pragma solidity =0.6.8;
import "./IEmpirePair.sol";
interface IEmpireFactory {
event PairCreated(
address indexed token0,
address indexed token1,
address pair,
uint256
);
function feeTo() external view returns (address);
function feeToSetter() external view returns (address);
function getPair(address tokenA, address tokenB)
external
view
returns (address pair);
function allPairs(uint256) external view returns (address pair);
function allPairsLength() external view returns (uint256);
function createPair(address tokenA, address tokenB)
external
returns (address pair);
function createPair(
address tokenA,
address tokenB,
PairType pairType,
uint256 unlockTime
) external returns (address pair);
function createEmpirePair(
address tokenA,
address tokenB,
PairType pairType,
uint256 unlockTime
) external returns (address pair);
function setFeeTo(address) external;
function setFeeToSetter(address) external;
}
// SPDX-License-Identifier: Unlicense
pragma solidity =0.6.8;
enum PairType {Common, LiquidityLocked, SweepableToken0, SweepableToken1}
interface IEmpirePair {
event Mint(address indexed sender, uint256 amount0, uint256 amount1);
event Burn(
address indexed sender,
uint256 amount0,
uint256 amount1,
address indexed to
);
event Swap(
address indexed sender,
uint256 amount0In,
uint256 amount1In,
uint256 amount0Out,
uint256 amount1Out,
address indexed to
);
event Sync(uint112 reserve0, uint112 reserve1);
function factory() external view returns (address);
function token0() external view returns (address);
function token1() external view returns (address);
function getReserves()
external
view
returns (
uint112 reserve0,
uint112 reserve1,
uint32 blockTimestampLast
);
function price0CumulativeLast() external view returns (uint256);
function price1CumulativeLast() external view returns (uint256);
function kLast() external view returns (uint256);
function sweptAmount() external view returns (uint256);
function sweepableToken() external view returns (address);
function liquidityLocked() external view returns (uint256);
function mint(address to) external returns (uint256 liquidity);
function burn(address to)
external
returns (uint256 amount0, uint256 amount1);
function swap(
uint256 amount0Out,
uint256 amount1Out,
address to,
bytes calldata data
) external;
function skim(address to) external;
function sync() external;
function initialize(
address,
address,
PairType,
uint256
) external;
function sweep(uint256 amount, bytes calldata data) external;
function unsweep(uint256 amount) external;
function getMaxSweepable() external view returns (uint256);
}
// SPDX-License-Identifier: Unlicense
pragma solidity =0.6.8;
// a library for performing overflow-safe math, courtesy of DappHub (https://github.com/dapphub/ds-math)
library EmpireMath {
function add(uint256 x, uint256 y) internal pure returns (uint256 z) {
require((z = x + y) >= x, "ds-math-add-overflow");
}
function sub(uint256 x, uint256 y) internal pure returns (uint256 z) {
require((z = x - y) <= x, "ds-math-sub-underflow");
}
function mul(uint256 x, uint256 y) internal pure returns (uint256 z) {
require(y == 0 || (z = x * y) / y == x, "ds-math-mul-overflow");
}
function min(uint256 x, uint256 y) internal pure returns (uint256 z) {
z = x < y ? x : y;
}
// babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
function sqrt(uint256 y) internal pure returns (uint256 z) {
if (y > 3) {
z = y;
uint256 x = y / 2 + 1;
while (x < z) {
z = x;
x = (y / x + x) / 2;
}
} else if (y != 0) {
z = 1;
}
}
}
// SPDX-License-Identifier: Unlicense
pragma solidity =0.6.8;
// a library for handling binary fixed point numbers (https://en.wikipedia.org/wiki/Q_(number_format))
// range: [0, 2**112 - 1]
// resolution: 1 / 2**112
library UQ112x112 {
uint224 private constant Q112 = 2**112;
// encode a uint112 as a UQ112x112
function encode(uint112 y) internal pure returns (uint224 z) {
z = uint224(y) * Q112; // never overflows
}
// divide a UQ112x112 by a uint112, returning a UQ112x112
function uqdiv(uint224 x, uint112 y) internal pure returns (uint224 z) {
z = x / uint224(y);
}
}